Improving amplify-and-forward relay selection algorithm based on partial relay link

The Journal of China Universities of Posts and Telecommunications February 2010, 17(1): 56–61 www.sciencedirect.com/science/journal/10058885

www.buptjournal.cn/xben

Improving amplify-and-forward relay selection algorithm based on partial relay link WANG Fei-fei ( ), LIU Yuan-an, LIN Xiao-feng, XIE Gang Key Laboraty of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract

This article addresses the design problem of selecting an appropriate relay in amplify-and-forward (AF) cooperative diversity systems. In this regard, this article focuses on relay selection based on partial channel knowledge only across the source and relay links. In particular, the two fundamental questions will be answered, that is, whether to cooperate and whom to cooperate with. Through answering these two questions, an improved relay selection strategy based on partial relay link, which emphasizes that cooperation happens when necessary, is proposed to aim at maximizing the average mutual information. Then a joint optimization, in terms of power allocation and relay selection, is employed to guarantee a robust performance for relay selection based on partial relay link. Optimum power is allocated between the source and the selected relay to maximize the output signal-to-noise (SNR) at the destination. Simulation results turn out that the improved scheme can achieve better performance than previous work and the robust performance can be guaranteed by employing joint optimization. Keywords cooperative diversity, amplify-and-forward relay, relay selection, average mutual information

1

Introduction

Cooperative diversity, which has promising application in future cellular, wireless LAN or Ad-hoc wireless communications systems, is a powerful idea to achieve spatial diversity without deploying multiple antennas at user node. Numerous research works have proved potentials of using cooperative diversity in wireless networks, such as in promising extended coverage, achieving spatial diversity through independent channels and saving energy through effective resource sharing [1–3]. Despite this, the effectiveness of cooperative diversity on network performance improvement heavily depends on selection of appropriate relay nodes from a set of potential candidates [1]. Because selecting unsuitable relay may not improve performance, and could even worsen the performance compared to the direct transmission. Therefore, the relay selection problem is crucial for cooperative network and has gained much research attention [4–6]. In Ref. [4], the authors

Received date: 29-11-2008 Corresponding author: WANG Fei-fei , E-mail: [email protected] DOI: 10.1016/S1005-8885(09)60424-6

proposed two relaying selection criteria based on the best instantaneous SNR of the whole links across the two-hops. Zhao Y et al. [5] proposed a selection AF based on having knowledge of all channel gains to minimize the outage probability. However, the above studies all require global channel knowledge including the source-relay and relaydestination channel coefficients, which introduce extra system overhead because of the connection to obtain these channel knowledge. On the other hand, collecting all the links of the networks is time sensitive to the delay effect; hence time synchronization among the nodes is a crucial issue for practical systems. The implementation complexity increases as the number of nodes increases. Therefore, the idea in Ref. [6] proposed AF relay selection based on partial channel knowledge only across source to relay links, which is relatively straightforward by monitoring the local connection rather than global connection and as a result it is easier to implement. This article focuses on AF relay selection based on partial relay link only across the source and the relay links. The authors propose a more reasonable optimization rule which emphasizes that cooperation happens when needed. Cooperation

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WANG Fei-fei , et al. / Improving amplify-and-forward relay selection algorithm based on partial relay link

is performed only when it outperforms the direct transmission. Otherwise, the direct transmission will be preferred. Although the similar optimization was considered in Ref. [7], which were based on global relay link including source to relay link and relay to destination link. It is shown that the proposed optimal scheme can improve the performance compared to the purely cooperation scheme in Ref. [6]. Additionally, it is recognized that the performance of the partial relay selection will be diminished as the relay node density increases. This is because increase in the relay node density can lead to increase the presence possibility of best SNR from source to the selected relay, as well as that of bad SNR from the selected relay to destination. Therefore, a joint optimization, in terms of power allocation and relay selection, is employed to guarantee robust performance. The remainder of the article is organized as follows. Sect. 2 outlines the system model for cooperative wireless network. In Sect. 3, an improved optimization rule is formulated to maximize the mutual information. Afterwards, joint power allocation and relay node selection is employed to guarantee robust performance. Finally, simulation results and conclusions are shown in Sects. 4 and 5, respectively.

2 System model and problem formulation 2.1

System model

Consider a wireless network with one source, one destination and N randomly deployed relay nodes as shown in Fig. 1. One interpretation of such network is the IEEE 802.16 point-to-multiple-point (PMP) network, where the source node represents the end users and the destination node represents the access point (AP) [7]. Link 1 means direct transmission, where the source transmits information to the destination directly. Link 2 means cooperative transmission, where the optimal relay is selected from the available relay set to forward information for the source.

Fig. 1 System model of relay network

Denote hsi and hid

as the channel from source to

ith relay and from ith relay to destination, respectively, which

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are modelled as integrated effects from both propagation path loss and fading. Then the channel from node i to node j is given by (1) hij = dij−γ Γ ij where Lij = dij−γ denotes the propagation path loss and dij denotes the distance between the transmitting node i and receiving node j, the fading Γ ij is an independent Rayleigh random variable with zero mean and unit variance. The cooperative protocol is based on the typical two-phase transmission. In the first phase, the source transmits the signal to the relays. In the second phase, the relays forward the received signal to the destination. Note that here the focus is on AF relay mode. The system model can be represented by the following two equations: ysi = Ps hsi x + nsi (2) yid = hid K i ysi + nid

(3)

where x, ysi and yid denote the source transmitted signal and received signals at the relay i and at the destination. Ps is the transmission power, the noises nsi and nid are independent identically distributed (i.i.d.) complex Gaussian random variables with variance N 0 . K i is an amplification factor, which is used to guarantee the transmission power of the relay node and satisfies Pi (4) Ki = 2 Ps hsi + N 0 Substituting Eqs. (2) and (4) into Eq. (3), one has Ps Pi Pi yid = hid hsi x + hid nsi + nid 2 2 Ps hsi + N 0 Ps hsi + N 0

(5)

where Pi denotes the transmission power of the ith relay. For simplicity, assume uniform power distribution Ps = Pi = P0 2 , where P0 denotes the total transmission power. In Ref. [7], the maximum mutual information for the cooperation has been formulated. Here it is noted that, different from Ref. [7], once the source successfully cooperates with the relay node, the direct link from the source to the destination does not contribute to the mutual information. Therefore, the maximum mutual information at the destination can be written as 2 2 ⎞ Ps Pi hsi hid 1 ⎛ ⎟= I coi = l b ⎜1 + 2 2 2 ⎝⎜ N 0 ( Ps hsi + Pi hid + N 0 ) ⎠⎟

⎞ 1 ⎛ Ps Piα siα id l b ⎜1 + ⎟ 2 ⎝ N 0 ( Psα si + Piα id + N 0 ) ⎠ where we have introduced the 2 2 α si = hsi , α id = hid for brevity.

(6) short-hand

notations

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Note that the single-relay cooperation is focused on. Although employing multiple relay nodes may improve the performance, it requires the additional resources and it would come along with increasing processing complexity. For direct transmission, no relay employed, the achievable average mutual information is calculated as

1 ⎛ P h I d = l b ⎜1 + s sd N0 2 ⎜⎝

2

2

⎞ 1 ⎛ Pα ⎞ 2 ⎟ = l b 1 + s sd ⎟ ⎟ 2 ⎜⎝ N0 ⎠ ⎠

(7)

where α sd = hsd . 2

The partial relay selection scheme is proposed in Ref. [6] where the best relay node is selected to maximize the SNR across the source to the relay. From Eq. (2), the selected relay j corresponding to maximum SNR can be written as j = arg min

i =1,2..., N

hsi

2

2

2

E( nsi )

= arg min

i =1,2..., N

hsi N0

(8)

The achievable mutual information of the system can be expressed as ⎞ Ps Pjα sjα jd 1 ⎛ I = I co = l b ⎜1 + (9) ⎟ ⎜ 2 ⎝ N 0 ( Psα sj + Pjα jd + N 0 ) ⎟⎠

3 3.1

Proposed algorithm Improved optimization problem

Designing effective relay node selection inevitably should address the following two questions: whether to cooperate and whom to cooperate with. Behind the two questions is the idea that there is no need for cooperation if the direct link, from the source to destination, is good enough to transmit information reliably, just as Link 1 in Fig. 1. Otherwise, the source will pick the optimal relay from all the candidate relays for cooperative transmission, just as Link 2 in Fig. 1. In Ref. [6], the simple AF relay selection based on partial relay link only focuses on relay cooperative link, while the direct transmission is ignored. Referring to the above two questions, the work in Ref. [6] only answers one question in terms of whom to cooperate with, but fails to consider whether to cooperate. Intuitively, taking account of two questions together is more rational and can provide better performance. This is the authors’ motivation to formulate an improved optimization problem to maximize the network capacity as follows. max{I co , I d } ⎫ ⎪ s.t. I co = max ε i I i ⎪ i∈Ω ⎪ (10) ⎬ ε 1 ≤ ∑ i ⎪ i∈Ω ⎪ ε i ∈ {0,1} ⎪⎭

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where ε i is an indicator function of relay node selection.

ε i = 1 means that relay node i is selected for the source and ε i = 0 otherwise. Ω = {1,2,..., N } denotes the set of all available relay nodes. The optimal solution Eq. (10) can ensure that cooperation happens only if it can achieve larger capacity than direct transmission. The detailed solution steps are described as follows. Step 1 Search all relays and select a relay which can provide the maximum mutual information. Step 2 Calculate the maximum mutual information of cooperation I co and that of direct transmission I d , respectively. Step 3 Determine and obtain the maximum mutual information of the system I = max{I co , I d } . Simulation results presented in Sect. 4 demonstrate the effectiveness of the improved optimal problem. Additionally, another interesting question is that the performance of the partial relay selection will be diminished as the relay node density increases. The reason for this is that increasing the relay node density can increase the presence possibility of best SNR from source to the selected relay, as well as that of bad SNR from the selected relay to destination. To conquer the above negative effect, a joint optimization, in terms of relay node selection and power allocation, can be employed to achieve robust performance. 3.2

Joint optimization problem

The joint optimization problem, which integrates relay node selection and power allocation to achieve robust performance, looks formidable and complex at a first glance as different combinations of power allocation and relay selection are operated together. Fortunately, Ref. [7] provides a tractable algorithm of the complex joint optimization problem by decoupling the problem into two subproblems. One is the relay node selection based on uniform power distribution. The other is the power optimization based on a selected relay. The work also demonstrates the effectiveness of the decoupling, which can reduce the computational complexity and achieve comparable performance with the optimal one. In Sect. 2, relay selection has been finished under the assumption of uniform power distribution between the source and the relay node. Then the emphasis will be on the power allocation between the selected relay node and the source. Based on the mutual information expression in Eq. (6), one is able to find that optimum power allocation is equal to

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WANG Fei-fei , et al. / Improving amplify-and-forward relay selection algorithm based on partial relay link

maximize the output instantaneous SNR at the destination. Define Ps Pjα sjα jd γ jd ( Ps , Pj ) = (11) N 0 ( Psα sj + Pjα jd + N 0 )

Then the optimal power allocation can be formulated as ⎫ max γ jd ( Ps , Pj ) ⎪ s.t. Ps + Pj = P0 ⎬ (12) ⎪ Ps , Pj≥0 ⎭ The relay power Pj can be substituted as a function of

Pj = P0 − Ps , thus the objective of optimization problem

d 2γ jd ( Ps ) dPs2

= 2 Aj B j Ps − 2 AjC j

Only if d 2γ jd ( Ps ) dPs2 < 0 , γ jd ( Ps )

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(19) can achieve its

maximum at Ps . Substituting Eq. (18) into Eq. (19), one can find that Ps2 satisfies the above analysis and belongs to the range of Ps2 ∈ (0, P0 ) . Then, the optimal source power infers

Ps = Ps2 and the relay power is Pj = P0 − Ps . As a summary, the whole operation of the proposed scheme is illustrated in Fig. 2.

Eq. (12) is a function of Ps only. Eq. (12) can be solved by taking the first-order derivative of its objective function (called γ jd ( Ps ) below) with respect to Ps and let it equate

to zero, one can get dγ jd ( Ps ) = Aj B j Ps2 − 2 AjC j Ps + P0 AjC j = 0 dPs

(13)

where the coefficients Aj , B j , C j are defined as

Aj = α sjα jd N 0

(14)

B j = α jd − α sj

(15)

C j = P0α jd + N 0

(16)

We can see that

dγ jd ( Ps ) dPs

polynomial function, which has real roots under the following condition: (17) Δ j = 4 A2j − 4 P0 A2j B j C j≥0 Substituting Eqs. (14) –(16) into Eq. (17) leads to the result Δ j≥0 . Based on the above analysis, one can obtain that Eq. (13) has two real roots Ps1 and Ps2 , respectively, and they are defined as Δj ⎫ C ⎪ Ps1 = j + B j 2 Aj B j ⎪ ⎬ Δj ⎪ Cj 2 Ps = − ⎪ B j 2 Aj B j ⎭

Fig. 2 Flow chart of the proposed scheme

is a second-order The proposed algorithm in this article has two main advantages compared with the purely cooperation based on partial relay selection. One is that the authors propose a more reasonable optimization scheme which emphasizes that cooperation happens when needed, which can improve the performance compared to the purely cooperation scheme or purely direct transmission. The other advantage is that the proposed algorithm can achieve robust performance by employing joint optimization in terms of power allocation and relay selection.

(18)

One solution to determine which of Ps1 and Ps2 can maximize γ jd ( Ps ) is based on the second derivative test in Ref. [8]. Theorem 1 Second derivative test: let f ( x ) be twice differentiable and let x = ξ be a stationary point, f ′(ξ ) = 0 . If f ′′(ξ ) < 0, then the point is a relative maximum; if f ′′(ξ ) > 0, then the point is a relative minimum; if f ′′(ξ ) = 0, then the test fails. With the second derivative test, one can get the following result

4

Simulation results

In this section simulation results are presented to demonstrate the effectiveness of the improved optimization algorithms. The computational results are verified by Monte Carlo simulations of the system using 105 samples. Unless otherwise mentioned, the path loss exponent γ equals to 2 in the simulation. SNR is represented by the ratio between the total transmission power and the variance of the noise, which is a more or less virtual SNR determining Ps , Pi and N 0 . The scenario in the simulation is emulated in Fig. 3, where the destination node is located at the centre of the circle, while 100 relay nodes are uniformly distributed in the covered

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area. The source node is assumed to be located at the edge of the coverage area. The radius of the circle area is 50 m.

Fig. 3

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interpretation for this is that increasing the relay node density can increase the presence possibility of best SNR from source to the selected relay, as well as that of bad SNR from the selected relay to destination. In Fig. 5, the performance comparison is shown between the proposed scheme and the previous work in Ref. [6] with optimal power allocation. One can see that both of them can achieve robust performance as the relay nodes increase. Another observation is that the performance improvement no longer increases on the condition of sufficiently large relay nodes. This is justifiable that only one relay node can be selected so that further increasing the relay node density cannot increase the presence of a best relay node.

The distribution of user nodes in the simulation

The average mutual information is illustrated Fig. 4, in terms of the number of relay nodes based on a uniform power distribution between the source and the relay node. For simplicity, optimal power allocation between the source node and the relay node is omitted first. Note that SNR is 30 dB. For illustration, AF relay selection scheme based on partial relay link is denoted by previous scheme [6]. The improved scheme Eq. (10) proposed in Subsection 3.1 is denoted by Improved scheme. From Fig. 4 it can be seen that the improved scheme achieves better performance than previous scheme [6]. Both of them have higher average mutual information compared to direct transmission as the relay node density increases. The achievable highest point representing the best performance is at approximate 20 relay nodes and the performance of both improved scheme and previous scheme will be diminished as the relay node density increases. The

Fig. 4 Average mutual information comparison among improved scheme, previous scheme, direct transmission at 30 dB SNR

Fig. 5 Average mutual information comparison among three schemes with optimal power allocation at 30 dB SNR

Fig. 6 shows the average mutual information improvement with respect to different values of SNR with 50 relay nodes. The result is identical with that in Fig. 5 where the performance of the proposed scheme comes first.

Fig. 6 Average mutual information comparison with the different value of SNR

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WANG Fei-fei , et al. / Improving amplify-and-forward relay selection algorithm based on partial relay link

Conclusions

This article analyzes AF relay selection based on partial channel knowledge only across the source and the relay links. The authors propose a more reasonable cooperative rule which emphasizes that cooperation happens when needed. It is demonstrated that the proposed scheme can improve the performance compared with the previous scheme. Also, it is found that robustness of the partial relay selection scheme can be guaranteed by employing the idea of joint optimization. Finally, the simulation results are presented to verify the analytical results.

2.

3.

4.

5.

Acknowledgements This work was supported by Sino-Swedish IMT-Advanced

6.

Cooperation Project (2008DFA11780), Canada-China Scientific and Technological Cooperation, the National Natural Science Foundation

7.

of China (60802033, 60873190), the Hi-Tech Research and Development Program of China (2008AA01Z211). 8.

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(Editor: WANG Xu-ying)